On the capacity and depth of compact surfaces

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2020-02-12 DOI:10.1007/s40062-020-00254-4

Mahboubeh Abbasi, Behrooz Mashayekhy

引用次数: 2

Abstract

K. Borsuk in 1979, at the Topological Conference in Moscow, introduced the concept of capacity and depth of a compactum. In this paper we compute the capacity and depth of compact surfaces. We show that the capacity and depth of every compact orientable surface of genus \(g\ge 0\) is equal to \(g+2\). Also, we prove that the capacity and depth of a compact non-orientable surface of genus \(g>0\) is \([\frac{g}{2}]+2\).

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关于密实曲面的容量和深度

1979年，K. Borsuk在莫斯科的拓扑会议上，引入了紧致的容量和深度的概念。本文计算了紧致曲面的容量和深度。证明了\(g\ge 0\)属的每一个紧致可定向曲面的容量和深度都等于\(g+2\)。并证明了属\(g>0\)的紧致非定向曲面的容量和深度为\([\frac{g}{2}]+2\)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.

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